Remark 4 Approximation properties of some summability methods in the classical and real Hardy spaces were considered by Oswald [1]}, Kryakin and Trebels [2]}, Storoienko [3]}, [4]} and for martingale Hardy spaces in Fridli, Manchanda and Siddiqi [5]} (see also [6]}, [7]}), Nagy [8]}, [9]}, [10]}, Tephnadze [11]}, [12]}, [13]}.

